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<H3>neb command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>neb etol ftol N1 N2 Nevery filename 
</PRE>
<UL><LI>etol = stopping tolerance for energy (energy units)
<LI>ftol = stopping tolerance for force (force units)
<LI>N1 = max # of iterations (timesteps) to run initial NEB 
<LI>N2 = max # of iterations (timesteps) to run barrier-climbing NEB
<LI>Nevery = print replica energies and reaction coordinates every this many timesteps
<LI>filename = file specifying final atom coordinates on other side of barrier 
</UL>
<P><B>Examples:</B>
</P>
<PRE>neb 0.1 0.0 1000 500 50 coords.final
neb 0.0 0.001 1000 500 50 coords.final 
</PRE>
<P><B>Description:</B>
</P>
<P>Perform a nudged elastic band (NEB) calculation using multiple
replicas of a system.  Two or more replicas must be used, two of which
are the end points of the transition path.
</P>
<P>NEB is a method for finding both the atomic configurations and height
of the energy barrier associated with a transition state, e.g. for an
atom to perform a diffusive hop from one energy basin to another in a
coordinated fashion with its neighbors.  The implementation in LAMMPS
follows the discussion in these 3 papers: <A HREF = "#Henkelman1">(Henkelman1)</A>,
<A HREF = "#Henkelman2">(Henkelman2)</A>, and <A HREF = "#Nakano">(Nakano)</A>.
</P>
<P>Each replica runs on a partition of one or more processors.  Processor
partitions are defined at run-time using the -partition command-line
switch; see <A HREF = "Section_start.html#start_7">Section_start 6</A> of the
manual.  Note that if you have MPI installed, you can run a
multi-replica simulation with more replicas (partitions) than you have
physical processors, e.g you can run a 10-replica simulation on one or
two processors.  You will simply not get the performance speed-up you
would see with one or more physical processors per replica.  See <A HREF = "Section_howto.html#howto_5">this
section</A> of the manual for further
discussion.
</P>
<P>NOTE: The current NEB implementation in LAMMPS restricts you to having
exactly one processor per replica.
</P>
<P>When a NEB calculation is performed, it is assumed that each replica
is running the same model, though LAMMPS does not check for this.
I.e. the simulation domain, the number of atoms, the interaction
potentials, and the starting configuration when the neb command is
issued should be the same for every replica.
</P>
<P>In a NEB calculation each atom in a replica is connected to the same
atom in adjacent replicas by springs, which induce inter-replica
forces.  These forces are imposed by the <A HREF = "fix_neb.html">fix neb</A>
command, which must be used in conjunction with the neb command.  The
group used to define the fix neb command specifies which atoms the
inter-replica springs are applied to.  These are the NEB atoms.
Additional atoms can be present in your system, e.g. to provide a
background force field or simply to hold fixed during the NEB
procedure, but they will not be part of the barrier finding procedure.
</P>
<P>The "starting configuration" for NEB should be a state with the NEB
atoms (and all other atoms) having coordinates on one side of the
energy barrier.  These coordinates will be assigned to the first
replica #1.  The coordinates should be close to a local energy
minimum.  A perfect energy minimum is not required, since NEB runs via
damped dynamics which will tend to drive the configuration of replica
#1 to a true energy minimum, but you will typically get better
convergence if the initial state is already at a minimum.  For
example, for a system with a free surface, the surface should be fully
relaxed before attempting a NEB calculation.
</P>
<P>The final configuration is specified in the input <I>filename</I>, which is
formatted as described below.  Only coordinates for NEB atoms or a
subset of them should be listed in the file; they represent the state
of the system on the other side of the barrier, at or near an energy
minimum.  These coordinates will be assigned to the last replica #M.
The final coordinates of atoms not listed in <I>filename</I> are set equal
to their initial coordinates.  Again, a perfect energy minimum is not
required for the final configuration, since the atoms in replica #M
will tend to move during the NEB procedure to the nearest energy
minimum.  Also note that a final coordinate does not need to be
specified for a NEB atom if you expect it to only displace slightly
during the NEB procedure.  For example, only the final coordinate of
the single atom diffusing into a vacancy need be specified if the
surrounding atoms will only relax slightly in the final configuration.
</P>
<P>The initial coordinates of all atoms (not just NEB atoms) in the
intermediate replicas #2,#3,...,#M-1 are set to values linearly
interpolated between the corresponding atoms in replicas #1 and #M.
</P>
<P>A NEB calculation has two stages, each of which is a minimization
procedure, performed via damped dynamics.  To enable this, you must
first define an appropriate <A HREF = "min_style.html">min_style</A>, such as
<I>quickmin</I> or <I>fire</I>.  The <I>cg</I>, <I>sd</I>, and <I>hftn</I> styles cannot be
used, since they perform iterative line searches in their inner loop,
which cannot be easily synchronized across multiple replicas.
</P>
<P>The minimizer tolerances for energy and force are set by <I>etol</I> and <I>ftol</I>, 
the same as for
the <A HREF = "minimize.html">minimize</A> command.
</P>
<P>A non-zero <I>etol</I>
means that the NEB calculation will terminate if the energy criterion is met 
by every replica.  The energies being compared to
<I>etol</I> do not include any contribution from the inter-replica forces, since
these are non-conservative.
A non-zero <I>ftol</I>
means that the NEB calculation will terminate if the force criterion is met 
by every replica.  The forces being compared to
<I>ftol</I> include the inter-replica forces between an atom and its images
in adjacent replicas.
</P>
<P>The maximum number of iterations in each stage is set by <I>N1</I> and
<I>N2</I>.  These are effectively timestep counts since each iteration of
damped dynamics is like a single timestep in a dynamics
<A HREF = "run.html">run</A>.  During both stages, the potential energy of each
replica and its normalized distance along the reaction path (reaction
coordinate RD) will be printed to the screen and log file every
<I>Nevery</I> timesteps.  The RD is 0 and 1 for the first and last replica.
For intermediate replicas, it is the cumulative distance (normalized
by the total cumulative distance) between adjacent replicas, where
"distance" is defined as the length of the 3N-vector of differences in
atomic coordinates, where N is the number of NEB atoms involved in the
transition.  These outputs allow you to monitor NEB's progress in
finding a good energy barrier.  <I>N1</I> and <I>N2</I> must both be multiples
of <I>Nevery</I>.
</P>
<P>In the first stage of NEB, the set of replicas should converge toward
the minimum energy path (MEP) of conformational states that transition
over the barrier.  The MEP for a barrier is defined as a sequence of
3N-dimensional states that cross the barrier at its saddle point, each
of which has a potential energy gradient parallel to the MEP itself.
The replica states will also be roughly equally spaced along the MEP
due to the inter-replica spring force added by the <A HREF = "fix_neb.html">fix
neb</A> command.
</P>
<P>In the second stage of NEB, the replica with the highest energy
is selected and the inter-replica forces on it are converted to a
force that drives its atom coordinates to the top or saddle point of
the barrier, via the barrier-climbing calculation described in
<A HREF = "#Hinkelman2">(Henkelman2)</A>.  As before, the other replicas rearrange
themselves along the MEP so as to be roughly equally spaced.
</P>
<P>When both stages are complete, if the NEB calculation was successful,
one of the replicas should be an atomic configuration at the top or
saddle point of the barrier, the potential energies for the set of
replicas should represent the energy profile of the barrier along the
MEP, and the configurations of the replicas should be a sequence of
configurations along the MEP.
</P>
<HR>

<P>A few other settings in your input script are required or advised to
perform a NEB calculation.
</P>
<P>An atom map must be defined which it is not by default for <A HREF = "atom_style.html">atom_style
atomic</A> problems.  The <A HREF = "atom_modify.html">atom_modify
map</A> command can be used to do this.
</P>
<P>The "atom_modify sort 0 0.0" command should be used to turn off atom
sorting.
</P>
<P>NOTE: This sorting restriction will be removed in a future version of
NEB in LAMMPS.
</P>
<P>The minimizers in LAMMPS operate on all atoms in your system, even
non-NEB atoms, as defined above.  To prevent non-NEB atoms from moving
during the minimization, you should use the <A HREF = "fix_setforce.html">fix
setforce</A> command to set the force on each of those
atoms to 0.0.  This is not required, and may not even be desired in
some cases, but if those atoms move too far (e.g. because the initial
state of your system was not well-minimized), it can cause problems
for the NEB procedure.
</P>
<P>The damped dynamics <A HREF = "min_style.html">minimizers</A>, such as <I>quickmin</I>
and <I>fire</I>), adjust the position and velocity of the atoms via an
Euler integration step.  Thus you must define an appropriate
<A HREF = "timestep.html">timestep</A> to use with NEB.  Using the same timestep
that would be used for a dynamics <A HREF = "run.html">run</A> of your system is
advised.
</P>
<HR>

<P>The specified <I>filename</I> contains atom coordinates for the final
configuration.  Only atoms with coordinates different than the initial
configuration need to be specified, i.e. those geometrically near the
barrier.
</P>
<P>The file can be ASCII text or a gzipped text file (detected by a .gz
suffix).  The file should contain one line per atom, formatted
with the atom ID, followed by the final x,y,z coordinates:
</P>
<PRE>125     24.97311   1.69005     23.46956
126     1.94691    2.79640     1.92799
127     0.15906    3.46099     0.79121
... 
</PRE>
<P>The lines can be listed in any order.
</P>
<HR>

<P>Four kinds of output can be generated during a NEB calculation: energy
barrier statistics, thermodynamic output by each replica, dump files,
and restart files.
</P>
<P>When running with multiple partitions (each of which is a replica in
this case), the print-out to the screen and master log.lammps file
contains a line of output, printed once every <I>Nevery</I> timesteps.  It
contains the timestep, the maximum force per replica, the maximum
force per atom (in any replica), potential gradients in the initial,
 final, and climbing replicas,  
the forward and backward energy barriers, 
the total reaction coordinate (RDT), and
the normalized reaction coordinate and potential energy of each replica.
</P>
<P>The "maximum force per replica" is
the two-norm of the 3N-length force vector for the atoms in each
replica, maximized across replicas, which is what the <I>ftol</I> setting
is checking against.  In this case, N is all the atoms in each
replica.  The "maximum force per atom" is the maximum force component
of any atom in any replica.  The potential gradients are the two-norm
of the 3N-length force vector solely due to the interaction potential i.e.
without adding in inter-replica forces. Note that inter-replica forces
are zero in the initial and final replicas, and only affect
the direction in the climbing replica. For this reason, the "maximum 
force per replica" is often equal to the potential gradient in the
climbing replica. In the first stage of NEB, there is no climbing
replica, and so the potential gradient in the highest energy replica
is reported, since this replica will become the climbing replica
in the second stage of NEB.
</P>
<P>The "reaction coordinate" (RD) for each
replica is the two-norm of the 3N-length vector of distances between
its atoms and the preceding replica's atoms, added to the RD of the
preceding replica. The RD of the first replica RD1 = 0.0; 
the RD of the final replica RDN = RDT, the total reaction coordinate.
The normalized RDs are divided by RDT,
so that they form a monotonically increasing sequence
from zero to one. When computing RD, N only includes the atoms 
being operated on by the fix neb command.
</P>
<P>The forward (reverse) energy barrier is the potential energy of the highest
replica minus the energy of the first (last) replica.
</P>
<P>When running on multiple partitions, LAMMPS produces additional log
files for each partition, e.g. log.lammps.0, log.lammps.1, etc.  For a
NEB calculation, these contain the thermodynamic output for each
replica.
</P>
<P>If <A HREF = "dump.html">dump</A> commands in the input script define a filename
that includes a <I>universe</I> or <I>uloop</I> style <A HREF = "variable.html">variable</A>,
then one dump file (per dump command) will be created for each
replica.  At the end of the NEB calculation, the final snapshot in
each file will contain the sequence of snapshots that transition the
system over the energy barrier.  Earlier snapshots will show the
convergence of the replicas to the MEP.
</P>
<P>Likewise, <A HREF = "restart.html">restart</A> filenames can be specified with a
<I>universe</I> or <I>uloop</I> style <A HREF = "variable.html">variable</A>, to generate
restart files for each replica.  These may be useful if the NEB
calculation fails to converge properly to the MEP, and you wish to
restart the calculation from an intermediate point with altered
parameters.
</P>
<P>There are 2 Python scripts provided in the tools/python directory,
neb_combine.py and neb_final.py, which are useful in analyzing output
from a NEB calculation.  Assume a NEB simulation with M replicas, and
the NEB atoms labelled with a specific atom type.
</P>
<P>The neb_combine.py script extracts atom coords for the NEB atoms from
all M dump files and creates a single dump file where each snapshot
contains the NEB atoms from all the replicas and one copy of non-NEB
atoms from the first replica (presumed to be identical in other
replicas).  This can be visualized/animated to see how the NEB atoms
relax as the NEB calculation proceeds.
</P>
<P>The neb_final.py script extracts the final snapshot from each of the M
dump files to create a single dump file with M snapshots.  This can be
visualized to watch the system make its transition over the energy
barrier.
</P>
<P>To illustrate, here are images from the final snapshot produced by the
neb_combine.py script run on the dump files produced by the two
example input scripts in examples/neb.  Click on them to see a larger
image.
</P>
<A HREF = "JPG/hop1.jpg"><IMG SRC = "JPG/hop1_small.jpg"></A>

<A HREF = "JPG/hop2.jpg"><IMG SRC = "JPG/hop2_small.jpg"></A>

<HR>

<P><B>Restrictions:</B>
</P>
<P>This command can only be used if LAMMPS was built with the REPLICA
package.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A> section
for more info on packages.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "prd.html">prd</A>, <A HREF = "temper.html">temper</A>, <A HREF = "fix_langevin.html">fix
langevin</A>, <A HREF = "fix_viscous.html">fix viscous</A>
</P>
<P><B>Default:</B> none
</P>
<HR>

<A NAME = "Henkelman1"></A>

<P><B>(Henkelman1)</B> Henkelman and Jonsson, J Chem Phys, 113, 9978-9985 (2000).
</P>
<A NAME = "Henkelman2"></A>

<P><B>(Henkelman2)</B> Henkelman, Uberuaga, Jonsson, J Chem Phys, 113,
9901-9904 (2000).
</P>
<A NAME = "Nakano"></A>

<P><B>(Nakano)</B> Nakano, Comp Phys Comm, 178, 280-289 (2008).
</P>
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